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B-metric spaces, fixed points and Lipschitz functionsFeb 08 2018The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of homogeneous type, ... More Order continuous operators on pre-Riesz spaces and embeddingsFeb 07 2018We investigate properties of order continuous operators on pre-Riesz spaces with respect to the embedding of the range space into a vector lattice cover or, in particular, into its Dedekind completion. We show that order continuity is preserved under ... More On fractional Hardy inequalities in convex setsFeb 07 2018We prove a Hardy inequality on convex sets, for fractional Sobolev-Slobodecki\u{\i} spaces of order $(s,p)$. The proof is based on the fact that in a convex set the distance from the boundary is a superharmonic function, in a suitable sense. The result ... More On the sum of projectors onto convex setsFeb 07 2018The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds. Our results ... More A note on supercyclic operators in locally convex spacesFeb 06 2018We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some examples are given. ... More Strong pseudo-amenability of some Banach algebrasFeb 06 2018In this paper we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some Matrix algebras. Using this tool, we characterize strong pseudo-amenability of $\ell^{1}(S)$, provided that $S$ is a uniformly ... More Shorted operators and minus orderFeb 06 2018Let $\mathcal{H}$ be a Hilbert space, $L(\mathcal{H})$ the algebra of bounded linear operators on $\mathcal{H}$ and $W \in L(\mathcal{H})$ a positive operator. Given a closed subspace $\mathcal{S}$ of $\mathcal{H}$, we characterize the shorted operator ... More Schauder bases and the decay rate of the heat equationFeb 06 2018We consider the classical Cauchy problem for the linear heat equation and integrable initial data in the Euclidean space $\mathbb{R}^N$. In the case $N=1$ we show that given a weighted $L^p$-space $L_w^p(\mathbb{R})$ with $1 \leq p < \infty$ and a fast ... More Localizing Weak Convergence in $\boldsymbol{ L_\infty}$Feb 06 2018For a general measure space $(X, \sL, \l)$ the pointwise nature of weak convergence in $\Li$ is investigated using singular functionals analogous to $\d$-functions in the theory of continuous functions on topological spaces. The implications for pointwise ... More Properties of the Space of Sections of Some Banach BundlesFeb 06 2018One shows for Banach bundles in a certain class that having a second countable locally compact Hausdorff base space and separable fibers implies the separability of the Banach space of the all sections that vanish at infinity. In the reverse direction, ... More Abstract Lorentz spaces and Köthe dualityFeb 05 2018Given a fully symmetric Banach function space $E$ and a decreasing positive weight $w$ on $I = (0, a)$, $0 < a \le \infty $, the generalized Lorentz space ${\Lambda}_{E,w}$ is defined as the symmetrization of the canonical copy $E_w$ of $E$ on the measure ... More Dunkl-Schrödinger operatorsFeb 05 2018In this paper, we consider the Schr\"odinger operators $L_k=-\Delta_k+V$, where $\Delta_k$ is the Dunkl-Laplace operator and $V$ is a non-negative potential on $R^d$. We establish that $L_k $ is essentially self-adjoint on $C_0^\infty$. In particular, ... More A study on downward half Cauchy sequencesFeb 05 2018In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function $f$ on a subset $E$ of $\R$, the set of real numbers is down continuous if it preserves downward half Cauchy sequences, i.e. the sequence ... More Reduced commutativity of moduli of operatorsFeb 03 2018In this paper, we investigate the question of when the equations $A^{*s}A^{s}=(A^{*}A)^{s}$ for all $s \in S$, where $S$ is a finite set of positive integers, imply the quasinormality or normality of $A$. In particular, it is proved that if $S=\{p,m,m+p,n,n+p\}$, ... More Entropy numbers of finite-dimensional embeddingsFeb 02 2018Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings $id:\ell_p^n\to ... More Embeddings for spaces of Lorentz-Sobolev typeJan 31 2018The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation between classes ... More On extreme contractions between real Banach spacesJan 30 2018We completely characterize extreme contractions between two-dimensional strictly convex and smooth real Banach spaces, perhaps for the very first time. In order to obtain the desired characterization, we introduce the notions of (weakly) compatible point ... More A characterization of nonnegativity relative to proper conesJan 30 2018Feb 06 2018Let $A$ be an $m \times n$ matrix with real entries. Given two proper cones $K_1$ and $K_2$ in $\mathbb{R}^n$ and $\mathbb{R}^m$, respectively, we say that $A$ is nonnegative (relative to $K_1$ and $K_2$) if $A(K_1) \subseteq K_2$. $A$ is said to be semipositive ... More Bounded multiplicative Toeplitz operators on sequence spacesJan 29 2018In this paper, we study the linear mapping which sends the sequence $x=(x_n)_{n \in \mathbb{N}}$ to $y=(y_n)_{n \in \mathbb{N}}$ where $y_n = \sum_{k=1}^\infty f(n/k)x_k$ for $f: \mathbb{Q}^+ \to \mathbb{C}$. This operator is the multiplicative analogue ... More Operational calculus for Fourier transform on the group $GL(2,R)$Jan 29 2018Consider the Fourier transform on the group $GL(2,R)$ of real $2\times 2$-matrices. We show that Fourier-images of polynomial differential operators on $GL(2,R)$ are differential-difference operators with coefficients meromorphic in parameters of representations. ... More Kirk's Fixed Point Theorem in Complete Random Normed modulesJan 29 2018Recently, stimulated by financial applications and $L^0$--convex optimization, Guo, et.al introduced the notion of $L^0$--convex compactness for an $L^0$--convex subset of a Hausdorff topological module over the topological algebra $L^0(\mathcal{F},K)$, ... More A Balian-Low Theorem for SubspacesJan 28 2018We extend the Balian-Low theorem to Gabor subspaces of $L^2(\mathbb R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating a subspace ... More Duality of Bochner spacesJan 27 2018Feb 01 2018We construct the generalized Lebesgue--Bochner spaces $L^p(\mu,\varPi)$ for positive measures $\mu$ and for suitable real or complex topological vector spaces $\varPi$ so that for $1<p<+\infty$ and Banachable $\varPi$ with separable topology the strong ... More After Plancherel formulaJan 26 2018We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation of non-uniform spectra. Our purpose is to indicate some non-solved problems ... More Concentration without measureJan 26 2018Although there doesn't exist the Lebesgue measure in the ball $M$ of $C[0,1]$ with $p-$norm, the average values (expectation) $EY$ and variance $DY$ of some functionals $Y$ on $M$ can still be defined through the procedure of limitation from finite dimension ... More New results about some inequalities for operator meansJan 25 2018Feb 05 2018New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator P\'olya-Szeg\"o inequality to arbitrary operator means. Furthermore, ... More Local extension property for finite height spacesJan 25 2018We introduce a new technique for the study of the local extension property (LEP) for boolean algebras and we use it to show that the clopen algebra of every compact Hausdorff space $K$ of finite height has LEP. This implies, under appropriate additional ... More On Weak Supercyclicity IJan 24 2018This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability. Sharp comparison of moments and the log-concave moment problemJan 23 2018This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors uniformly distributed ... More Multivariable Bergman shifts and Wold decompositionsJan 23 2018Let $H_m(\mathbb B)$ be the analytic functional Hilbert space on the unit ball $\mathbb B \subset \mathbb C^n$ with reproducing kernel $K_m(z,w) = (1 - \langle z,w \rangle)^{-m}$. Using algebraic operator identities we characterize those commuting row ... More On the Existence of Normal Square and Nth Roots of OperatorsJan 21 2018Jan 24 2018The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any operator $T$ is ... More Global and Concrete Quantizations on General Type I GroupsJan 21 2018In recent papers and books, a global quantization has been developed for {\it unimodular} groups of type I\,. It involves operator-valued symbols defined on the product between the group $\G$ and its unitary dual $\wG$\,, composed of equivalence classes ... More Nonlinear operations on a class of modulation spacesJan 21 2018We discuss when the nonlinear operation $f\mapsto F(f)$ maps the modulation space $M^{p,q}_s(\mathbb{R}^n)$ ($1 \leq p,q \leq \infty$) to the same space again. It is known that $M^{p,q}_s(\mathbb{R}^n)$ is a multiplication algebra when $s > n-n/q$, hence ... More Vector valued Hardy spacesJan 20 2018The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have ... More Linear space properties of $H^p$ spaces of Dirichlet seriesJan 19 2018We study $H^p$ spaces of Dirichlet series, called $\mathcal{H}^p$, for the range $0<p< \infty$. We begin by showing that two natural ways to define $\mathcal{H}^p$ coincide. We then proceed to study some linear space properties of $\mathcal{H}^p$. More ... More Eventually Entanglement Breaking MapsJan 17 2018We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor ... More Graph Laplace and Markov operators on a measure spaceJan 13 2018The main goal of this paper is to build a measurable analogue to the theory of weighted networks on infinite graphs. Our basic setting is an infinite $\sigma$-finite measure space $(V, \mathcal B, \mu)$ and a symmetric measure $\rho$ on $(V\times V, \mathcal ... More Homogeneous length functions on groupsJan 11 2018A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell : G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant \ell(x) + \ell(y)$ ... More The Petersen graph has no quantum symmetryJan 09 2018Jan 17 2018In 2007, Banica and Bichon asked whether the well-known Petersen graph has quantum symmetry. In this article, we show that the Petersen graph has no quantum symmetry, i.e. the quantum automorphism group of the Petersen graph is its usual automorphism ... More Fixed Points of anti-attracting maps and Eigenforms on FractalsJan 08 2018An important problem in analysis on fractals is the existence of a self-similar energy on finitely ramified fractals. The self-similar energies are constructed in terms of eigenforms, that is, eigenvectors of a special nonlinear operator. Previous results ... More On Absolutely Norm attaining OperatorsJan 08 2018We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately. Finally, we ... More Frobenius Theorem in Banach SpaceJan 04 2018Let $\Lambda$ be an open set in Banach space $E$, $M(x)$ for $x\in \Lambda$ a subspace in $E$, and $\mathcal F=\{M(x)\}_{x\in\Lambda}$. In this paper, we introduce the concept of the co-final set $J(x_0,E_*)$ for $\mathcal F$ at $x_0\in \Lambda$, then ... More Moment measures and stability for Gaussian inequalitiesDec 30 2017Let $\gamma$ be the standard Gaussian measure on $\mathbb{R}^n$ and let $\mathcal{P}_{\gamma}$ be the space of probability measures that are absolutely continuous with respect to $\gamma$. We study lower bounds for the functional $\mathcal{F}_{\gamma}(\mu) ... More On weighted polynomial approximationDec 26 2017Let $\varPhi:{\mathbb R}^n \to [1, \infty)$ be a semi-continuous from below function such that $\lim \limits_{x \to \infty} \displaystyle \frac {\ln \varPhi(x)} {\Vert x \Vert} = +\infty$. It is shown that polynomials are dense in $C_{\varPhi}({\mathbb ... More A priori estimates for the Fitzpatrick functionDec 26 2017New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space. On embeddings of locally finite metric spaces into $\ell_p$Dec 21 2017It is known that if finite subsets of a locally finite metric space $M$ admit $C$-bilipschitz embeddings into $\ell_p$ $(1\le p\le \infty)$, then for every $\epsilon>0$, the space $M$ admits a $(C+\epsilon)$-bilipschitz embedding into $\ell_p$. The goal ... More Moment infinitely divisible weighted shiftsOct 29 2017We say that a weighted shift $W_\alpha$ with (positive) weight sequence $\alpha: \alpha_0, \alpha_1, \ldots$ is {\it moment infinitely divisible} (MID) if, for every $t > 0$, the shift with weight sequence $\alpha^t: \alpha_0^t, \alpha_1^t, \ldots$ is ... More Weyl's Theorem for pairs of commuting hyponormal operatorsOct 29 2017Let $\mathbf{T}$ be a pair of commuting hyponormal operators satisfying the so-called quasitriangular property $$ \textrm{dim} \; \textrm{ker} \; (\mathbf{T}-\boldsymbol\lambda) \ge \textrm{dim} \; \textrm{ker} \; (\mathbf{T} - {\boldsymbol\lambda})^*), ... More A new approach to the nonsingular cubic binary moment problemOct 29 2017We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment matrices to deal ... More Derivations of Group AlgebrasAug 16 2017In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group. A non-linear Bishop-Phelps-Bollobás type theoremJul 21 2017The main aim of this paper is to prove a Bishop-Phelps-Bollob\'as type theorem on the unital uniform algebra A_{w^*u}(B_{X^*}) consisting of all w^*-uniformly continuous functions on the closed unit ball B_{X^*} which are holomorphic on the interior of ... More Fourth moment theorems on the Poisson space in any dimensionJul 06 2017We extend to any dimension the quantitative fourth moment theorem on the Poisson setting, recently proved by C. D\"obler and G. Peccati (2017). In particular, by adapting the exchangeable pairs couplings construction introduced by I. Nourdin and G. Zheng ... More Generalization Properties of Doubly Online Learning AlgorithmsJul 03 2017Doubly online learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning sequence may not be in ... More Quantum Symmetries of Graph C*-AlgebrasJun 27 2017The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple ... More Aluthge transforms of 2-variable weighted shiftsJun 11 2017We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, ... More $M$-ideal properties in Orlicz-Lorentz spacesMay 30 2017Jun 28 2017We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $\Lambda_{\varphi,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, ... More